2 Plan Contexte et motivations Méthodes et données RésultatsEnjeux et imagerie TEP/TDM (PET/CT)Objectif et état de l’artMéthodes et donnéesApproches développéesDonnées de validation et analyseRésultatsOptimisationRésultats et applicationsDiscussion et perspectivesAnd here is the outline of my talk. I’ll state the motivation and objective of this work, then l’ll talk about PET image segmentation. I’ll will then present the results we obtained on various datasets, and finally I will conclude and present the studies in progress2

4 Contexte et motivationsImagerie TEPPrincipes physiques de la TEPTEP (Tomographie par Emission de Positons)Principe de base :détection de l’annihilation d’un positon (+) et d’un électron (-)ReconstructionAnneaux de détecteursCoïncidences‘lignes de réponse’And here is the outline of my talk. I’ll state the motivation and objective of this work, then l’ll talk about PET image segmentation. I’ll will then present the results we obtained on various datasets, and finally I will conclude and present the studies in progress1 à 3 mm180°+/- 0.25°4

5 Contexte et motivationsImagerie TEP/TDM (PET/CT)Imagerie multi-modalité et fusionScanner à rayons X (TDM) et scanner TEP avec un seul lit d’examenAnd here is the outline of my talk. I’ll state the motivation and objective of this work, then l’ll talk about PET image segmentation. I’ll will then present the results we obtained on various datasets, and finally I will conclude and present the studies in progressPhilips GEMINISiemens BiographGE Discovery LS5

6 Contexte et motivationsImagerie TEP/TDM (PET/CT)Imagerie multi-modalité et fusionAnd here is the outline of my talk. I’ll state the motivation and objective of this work, then l’ll talk about PET image segmentation. I’ll will then present the results we obtained on various datasets, and finally I will conclude and present the studies in progress6

14 Plan Contexte et motivations Méthodes et données RésultatsEnjeux et imagerie TEP/TDM (PET/CT)Objectif et état de l’artMéthodes et donnéesApproches développéesDonnées de validation et analyseRésultatsOptimisationRésultats et applicationsDiscussion et perspectivesAnd here is the outline of my talk. I’ll state the motivation and objective of this work, then l’ll talk about PET image segmentation. I’ll will then present the results we obtained on various datasets, and finally I will conclude and present the studies in progress14

15 Méthodes et données Méthodes développéesHypothèse de travailL’objet d’intérêt à segmenter est déjà identifié et isolé dans une boîte de sélectionAnd here is the outline of my talk. I’ll state the motivation and objective of this work, then l’ll talk about PET image segmentation. I’ll will then present the results we obtained on various datasets, and finally I will conclude and present the studies in progressLa boîte de sélection doit :Contenir l’objet entierContenir suffisamment de fondElle n’est pas forcément cubique15

17 Méthodes et données Méthodes développées Contexte méthodologiqueL’aspect probabiliste et statistique permet de prendre en compte l’incertitude de la classificationL’aspect flou permet de modéliser l’imprécision inhérente aux données acquisesCombiner les deux permet de prendre en compte l’aspect bruité et flou des images d’émission: Mesure de Dirac sur la classe cModélisation standard “dure”Ground-truth[1] H. Caillol et al, IEEE Transactions on Geoscience Remote Sensing, 1993[2] F. Salzenstein and W. Pieczynski, Graphical Models and Image Processing, 1997: Mesure continue de Lesbegue surModélisation floue [1,2]Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlySeulement deux classes dures17

18 Méthodes et données Méthodes développées … … Chaînes de Markov flouesDéfinitionsMéthodes et donnéesHypothèse de Markov :Probabilités de transitionProbabilités initiales……Attache aux donnéesPour passer de l’image (2D ou 3D) à la chaîne (1D), on utilise un parcours fractal d’Hilbert-Peano [1]tout pixel de la chaîne possède comme voisins, deux pixels voisins sur l’image (pas l’inverse)Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only[1] S. Kamata, et al, IEEE Transactions on Image Processing, 199918

19 Méthodes et données Méthodes développéesChaînes de Markov flouesLoi a prioriMéthodes et donnéesDans le contexte d’une chaîne floue, chaque prend ses valeurs dansHypothèse de chaîne stationnaire. Les densités a priori peuvent être déduites d’une densité jointe définie sur le couple [1]Densités de transitionsNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyAvec :Densités initiales[1] F. Salzenstein, C. Collet, S. Lecam, M. Hatt, Pattern Recognition Letters, 200719

20 Méthodes et données Méthodes développées Loi des observations :Chaînes de Markov flouesLoi des observationsMéthodes et donnéesLoi des observations :En pratique on opère une discrétisation de l’intervalle [1]On définit alors un certain nombre de niveaux de flou avec des valeurs associées2 classes dures 0 et 1 de moyennes et variancespour chaque niveau de flou, on détermine les moyennes et variances :Nombre de niveaux de flou et valeurs associées à définirNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyPour chaque classe dure on peut définir les distributions comme gaussiennes ou d’autres distributions avec le système de Pearson [2][1] F. Salzenstein, C. Collet, S. Lecam, M. Hatt, Pattern Recognition Letters, 2007[2] Y. Delignon, et al, IEEE Transactions on Image Processing, 199720

21 Méthodes et données Méthodes développéesChaînes de Markov flouesSegmentation MPMMéthodes et donnéesSegmentation avec le critère MPM [1] adapté au cas flou [2] :la décision bayésienne affectant une étiquette à chaque élément t correspond à :où est une fonction de coûten pratique cela revient à minimiser la fonction :Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyCe qui nécessite le calcul des densités a posteriori[1] J. Maroquin et al, Journal of the American Statistical Association, 1987[2] F. Salzenstein and W. Pieczynski, Graphical Models and Image Processing, 199721

22 Méthodes et données Méthodes développéesChaînes de Markov flouesProcédure forward-backwardMéthodes et donnéesProcédures forward-backward : calcul récursif direct sur la chaîne [1]…Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only[1] P. Devijver, Pattern Recognition Letters, 198522

23 Méthodes et données Méthodes développéesChaînes de Markov flouesEstimation SEMMéthodes et donnéesEstimation itérative SEM (Stochastic Expectation Maximization) [1]estimation empirique des paramètres par la méthode des momentssur une réalisation a posteriori de X qu’il faut simulerUtilisation des calculs forward-backward pour la simulation:premier élément :transitions :Estimation de tous les paramètres sur cette réalisation :Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only[1] G. Celeux et J. Diebolt, Revue de statistique appliquée, 198623

24 Méthodes et données Méthodes développéesChaînes de Markov flouesRésuméMéthodes et donnéesVecteur 1D à valeurs réelles : YHilbert-Peano 3DEstimation stochastique (SEM)Paramètres estimés :Modèle a priori (probabilités initiales et de transitions)Modèle de bruit (moyennes et variances)Image 3DHilbert-Peano 3D inverseCarte de segmentationNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyVecteur 1D à valeurs dans {0,1,F1,F2} : XSegmentation (MPM)[1] M. Hatt et al, Physics in Medicine and Biology, 200724

25 Méthodes et données Méthodes développéesApproche locale adaptative (FLAB)Loi a priori et loi des observationsMéthodes et donnéesChaque prend toujours ses valeurs dansPas d’hypothèse de Markov : modèle local et non globalProbabilités a priori [1] [2] :Indicés par t : prise en compte de la position dans l’imageLoi des observations : identique au cas des chaînesNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only[1] H. Caillol et al, IEEE Transactions on Geoscience Remote Sensing, 1993[2] M. Hatt et al, IEEE Transactions on Medical Imaging, 200825

26 Méthodes et données Méthodes développéesApproche locale adaptative (FLAB)Estimation SEM et segmentationMéthodes et donnéesOn utilise le même principe d’estimation que dans le cas des chaînesNécessité de calculer les probabilités a posteriori de chaque [1] [2] :On peut alors générer une réalisation a posteriori et estimer les paramètres :Cube centré sur le voxel t. Taille à définir !Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyInformation contextuelle prise en compte dans l’estimationOn peut également les utiliser pour la segmentation :Calculer pour chaque voxel la probabilité a posterioriSi elle est maximale avec c = 1 ou c = 0, affecter la classe 1 ou 0Sinon, choisir le niveau de flou qui maximise[1] H. Caillol et al, IEEE Transactions on Geoscience Remote Sensing, 1993, [2] M. Hatt et al, IEEE Transactions on Medical Imaging, 200826

27 Méthodes et données Méthodes développéesApproche locale adaptative (FLAB)Extension à trois classes duresMéthodes et donnéesOn modélise les mélanges entre chaque paire de classes dures uniquement132Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyM. Hatt et al, IEEE NSS-MIC conference records, 2007 & 2008Brevet : FR08 / 5608927

28 Méthodes et données Méthodes développées Probabilités a priori :Approche locale adaptative (FLAB)Extension à trois classes duresMéthodes et donnéesProbabilités a priori :AB transition floue entre classes dures A et BLoi des observationsNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyM. Hatt et al, IEEE NSS-MIC conference records, 2007 & 2008Brevet : FR08 / 5608928

29 Méthodes et données Méthodes développées Probabilités a posteriori :Approche locale adaptative (FLAB)Extension à trois classes duresMéthodes et donnéesProbabilités a posteriori :Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyOn peut alors générer une réalisation a posteriori et estimer les paramètres puis segmenter comme dans le cas binaireM. Hatt et al, IEEE NSS-MIC conference records, 2007 & 2008Brevet : FR08 / 5608929

30 Méthodes et données Méthodes développées Estimation stochastique (SEM)Approche locale adaptative (FLAB)RésuméMéthodes et donnéesEstimation stochastique (SEM)Paramètres estimés :Modèle a priori (probabilités pour chaque voxel)Modèle de bruit (moyennes et variances)Image 3DCarte de segmentation(chaînes)SegmentationCarte de segmentationNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyM. Hatt et al, IEEE NSS-MIC conference records, 2007 & 2008M. Hatt et al, IEEE Transactions on Medical Imaging, 200830

31 Méthodes et données Méthodes développées Carte de segmentationExploitation de la carte de segmentationCarte de segmentationVolume fonctionnelRegroupementNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyNiveaux de flou associés aux voxels affectés par les effets de volume partiel (EVP) :Voxels du fond dont la valeur a été rehausséeVoxels de l’objet dont la valeur a été diminuéeM. Hatt et al, IEEE NSS-MIC conference records, 2007M. Hatt et al, IEEE Transactions on Medical Imaging, 200831

32 Méthodes et données Données de validationObjectifs et analysePrécédentes publications : lacunes sur la validationUtilisation de données simulées ou de fantômes peu réalistes uniquementAbsence de considération de paramètres importants (taille de voxel, bruit, système…)Utilisation de données cliniques sans vérité terrain connueMesures de performances parfois peu pertinentesNous voulons valider sur des objets de synthèse et simulés réalistes, sur des acquisitions réelles, et sur des données cliniques pour lesquelles une vérité terrain est disponibleMesure de performance :Vérité terrainImage TEPSegmentationErreursErreur de volume :Erreur de classif. globale :Erreur de classif. :Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only32

33 Méthodes et données Données de validationFantômeSphères de diamètre 37, 28, 22, 17, 13 et 10 mmNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only33

34 A = 4:1 or 5:1, B = 8:1 or 10:1 1 = 2x2 mm, 2 = 4x4 or 5x5 mmMéthodes et donnéesDonnées de validationFantôme : acquisitionsParamètres considérés :contraste sphère/fond : de 4/1 à 10/1durée d’acquisition : 1, 2 et 5 mintaille du voxel : de 2 à 5 mm de côtéScanners (Philips et Philips TF, GE, Siemens) et algorithmes associés (RAMLA, TF MLEM et OSEM) avec protocoles cliniques standardsPhilips GeminiGE Discovery LSOSEMSiemens BiographRAMLAPhilips Gemini TFTF MLEMAB12A = 4:1 or 5:1, B = 8:1 or 10: = 2x2 mm, 2 = 4x4 or 5x5 mmNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only34

35 Méthodes et données Données de validation Philips GEMINI (RAMLA)Fantôme : acquisitionsPhilips GEMINI (RAMLA)Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only35

36 Méthodes et données Données de validation Vérité terrainObjets synthétiquesVérité terrainNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyContraste 10:5:1Bruit faibleContraste 10:5:1Bruit fortContraste 10:7:4Bruit faibleContraste 10:7:4Bruit fortFWHM environ 6 mmVoxels 2x2x2 mm336

37 (Non-Uniform Rational Basis Splines)Méthodes et donnéesDonnées de validationTumeurs simulées : procédureFantôme NCAT(NURBS)IncorporationModèle de scanner TEP+Contours manuelsVérité terrainTumeur NURBS(Non-Uniform Rational Basis Splines)RhinocerosTMTEPImage de patientSimulation GATEet reconstructionImage simuléeCalcul d’erreursNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyTDMSegmentationCarte de segmentationTumeur simuléeExtraction de tumeur37

38 Méthodes et données Données de validationTumeurs simulées : exemples20 tumeurs (pulmonaires, ORL, hépatiques)diamètre maximum de 12 à 82 mmHétérogénéité : de aucune à forteFormes : certaines presque sphériques, d’autres de formes complexesGrande et hétérogèneCliniqueSimuléeCliniqueSimuléePetite et homogèneNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only38

39 Méthodes et données Données de validationTumeurs réelles et histologie18 tumeurs (pulmonaires) ayant fait l’objet d’une étude macroscopique [1]diamètre maximum de 15 à 90 mm (moyenne 44, écart type 21)Hétérogénéité : de aucune à forteFormes : certaines presque sphériques, d’autres de formes complexesTDMTEPNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only[1] A. Van Baardwijk, et al, International Journal of Radiation Oncology Biolology Physics, 200739

40 Méthodes et données Données de validation 1 2 3 4 Temps Cas 1 8:4:1Suivi thérapeutique : 8 cas1234TempsCas 18:4:18:4:110:7:112:1Cas 34:14:2,5:12,5:11,5:1Cas 54:16:17:2:17.5:0.5:1Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyCas 68:16,5:14:13:140

41 Plan Contexte et motivations Méthodes et données RésultatsEnjeux et imagerie TEP/TDM (PET/CT)Objectif et état de l’artMéthodes et donnéesApproches développéesDonnées de validation et analyseRésultatsOptimisationRésultats et applicationsDiscussion et perspectivesAnd here is the outline of my talk. I’ll state the motivation and objective of this work, then l’ll talk about PET image segmentation. I’ll will then present the results we obtained on various datasets, and finally I will conclude and present the studies in progress41

42 Résultats Optimisation Paramètres à optimiser :Nombre de niveaux de flou et valeurs associéesType de distribution utilisé pour les observationsTaille du cube d’estimation (FLAB uniquement)Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only2 min1 min5 min42

43 Résultats Optimisation Les meilleurs résultats sont obtenus avec :ParamètresLes meilleurs résultats sont obtenus avec :2 niveaux de flou par transition, avec valeurs etNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyM. Hatt et al, Physics in Medicine and Biology, 200743

44 Résultats Optimisation Les meilleurs résultats sont obtenus avec :ParamètresLes meilleurs résultats sont obtenus avec :Distributions gaussiennes (le système de Pearson détecte des lois bêta mais sans amélioration significative des résultats)Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyM. Hatt et al, IEEE Transactions on Medical Imaging, 200844

45 Résultats Optimisation Les meilleurs résultats sont obtenus avec :ParamètresLes meilleurs résultats sont obtenus avec :Cube de taille 3x3x3 (pour FLAB)Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyM. Hatt et al, IEEE Transactions on Medical Imaging, 200845

46 Résultats OptimisationReproductibilitéSur cinq acquisitions indépendantes de 1 min chacuneEcart type sur les 5 réalisationsNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyM. Hatt et al, IEEE Transactions on Medical Imaging, 200846

47 Résultats Optimisation Sur sphères homogènes (4x4x4 mm3) (2x2x2 mm3)FLAB contre chaînes (FHMC)Sur sphères homogènes(4x4x4 mm3)(2x2x2 mm3)Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyM. Hatt et al, IEEE Transactions on Medical Imaging, 200847

48 Résultats Résultats sur sphèresRobustesse (et précision)Sur l’ensemble des acquisitions de fantôme (tous scanners, algorithmes, paramètres…)Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyM. Hatt et al, IEEE NSS-MIC conference records, 200848

49 Résultats Résultats sur objets synthétiques Vérité terrainNon binairesVérité terrainContraste 10:5:1Bruit faibleContraste 10:5:1Bruit fortContraste 10:7:4Bruit faibleContraste 10:7:4Bruit fortT4220 %23 %31 %27 %Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyT5083 %85 %8 %9 %49

50 Résultats Résultats sur objets synthétiques Vérité terrainNon binairesVérité terrainContraste 10:5:1Bruit faibleContraste 10:5:1Bruit fortContraste 10:7:4Bruit faibleContraste 10:7:4Bruit fortTbckg15 %17 %90 %38 %Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only21 %42 %21 %25 %TSBR50

51 Résultats Résultats sur objets synthétiques Non binairesC2C3Vérité terrainContraste 10:5:1Bruit faibleContraste 10:5:1Bruit fortContraste 10:7:4Bruit faibleContraste 10:7:4Bruit fortC2 : 11 %C3 : 21 %C2 : 13 %C3 : 19 %C2 : 18 %C3 : 45 %C2 : 30 %C3 : 84 %FCMNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyEC : 4.9 %EC : 7.6 %EC : 6.5 %EC : 9.9 %C2 : 7 %C3 : 7 %C2 : 9 %C3 : 15 %C2 : 9 %C3 : 19 %C2 : 12 %C3 : 27 %FLABEC : 4.4 %EC : 6.3 %EC : 4.2 %EC : 6.1 %51

52 Résultats Résultats sur objets synthétiques Non binaires FCMNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyVérité terrainFLAB52

53 Résultats Résultats sur tumeurs simulées Exemples Seuillage 42%Seuillage adaptatifFLAB(2 classes)SegmentationErreur de classificationVérité terrainTEP simulée> 100%14%6%Erreur de classificationC2 : 4%C3 : 2%Erreur de volume-62%+37%SegmentationVérité terrainTEP simuléeFLAB (3 classes)Seuillage 42%Seuillage adaptatifC3C2Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyM. Hatt et al, IEEE NSS-MIC conference records, 200853

54 Résultats Résultats sur tumeurs simuléesSur l’ensemble des vingt tumeursNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyM. Hatt et al, IEEE NSS-MIC conference records, 200854

55 Résultats Résultats sur tumeurs simuléesSur cas de suivi thérapeutiqueNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only55

56 Résultats Résultats sur tumeurs simuléesSur cas de suivi thérapeutiqueNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only56

57 Résultats Résultats sur tumeurs simuléesSur cas de suivi thérapeutiqueNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only57

58 Résultats Résultats sur tumeurs simuléesSur cas de suivi thérapeutiqueNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects only58

59 Résultats Résultats sur tumeurs réelles CT Threshold 42% PETavec histologie : exempleCTThreshold 42%Now a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyPETSegmentationFLABAdaptive thresholdM. Hatt et al, IEEE NSS-MIC conference records, 200859

60 Résultats Résultats sur tumeurs réellesavec histologie : sur l’ensemble des 18 tumeursNow a few words about the fuzzy modeling. On the one hand, the statistical part of the approach models the uncertainty of the classification. On the other hand, the fuzzy part models the imprecision of the acquired data. We combine both parts in order to model PET images characteristics. The statistical measure used in the classical modeling is the following sum of Dirac measures on each class, like illustrated here on a simple ground-truth, and with an associated noisy version of the image and its histogram. In the fuzzy model, we consider two Dirac measures for two hard classes 0 and 1, and a continuous Lesbegue measure on the interval in between to model the distribution of the fuzzy mixture. We called this algorithme FLAB for FUZZY locally adaptive bayesian. Unfortunately this modeling suffers from the limitation of being able to consider two hard classes only, hence homogeneous objects onlyM. Hatt et al, IEEE NSS-MIC conference records, 200860

61 Plan Contexte et motivations Méthodes et données RésultatsEnjeux et imagerie TEP/TDM (PET/CT)Objectif et état de l’artMéthodes et donnéesApproches développéesDonnées de validation et analyseRésultatsOptimisationRésultats et applicationsDiscussion et perspectivesAnd here is the outline of my talk. I’ll state the motivation and objective of this work, then l’ll talk about PET image segmentation. I’ll will then present the results we obtained on various datasets, and finally I will conclude and present the studies in progress61

63 Discussion et perspectivesQuantificationObtenir le volume exact ne suffit pas !Nécessité de combiner avec la correction quantitative des effets de volume partiel (méthode de Rousset ou MMA)To conclude, we have developed a fully automatic approach for volume determination in PET. It is capable of handling non homogeneous uptake and non spherical shapes, and also providing non binary segmented volumes, which can be useful for example for dose painting applications. Its robustness was evaluated using multiple phantom acquisitions demonstrating the algorithm does not require specific system-dependent optimization. Its accuracy was assessed on both simulated and real tumour.63